Electrical characterization and modelling of round spiral supercapacitors for high power applications

HAL Id: hal-00411480

https://hal.archives-ouvertes.fr/hal-00411480

Submitted on 27 Aug 2009

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Electrical characterization and modelling of round spiral supercapacitors for high power applications

A. Hammar, R. Lallemand, Pascal Venet, G. Coquery, Gérard Rojat, J.

Chabas

To cite this version:

A. Hammar, R. Lallemand, Pascal Venet, G. Coquery, Gérard Rojat, et al.. Electrical characterization and modelling of round spiral supercapacitors for high power applications. ESSCAP’06, Nov 2006, Lausanne, Switzerland. pp.on CD. �hal-00411480�

Electrical characterization and modelling of round spiral supercapacitors for high power applications

A. Hammar *, R. Lallemand**, P. Venet***, G. Coquery**, G. Rojat***, J. Chabas*

*SNCF Direction de la Recherche, Paris

** INRETS Laboratoire des Technologies Nouvelles, Arcueil

***CEGELY UCB Lyon

Abstract

Our laboratory research project consists on the study of accelerating cycling and ageing of supercapacitors under railway and electrical traction constraints. Electrical model parameters according to physical and electrochemical phenomena represent an important key to investigate aging indicators of supercapacitors and give precious information on its state of health. These kinds of studies need a powerful techniques and instrumentations.

Nowadays several electrical characterization methods exist. We have chosen to use two complementary methods: impedance spectroscopy and direct current charge/discharge methods. The present work describes the metrology defined to electrical characterization of supercapacitors. Electrical modelling based on simple tortuous pore impedance is explained. Some electrical parameters of the model defined for winded supercapacitors are investigated for different temperatures and different voltages. Finally, we have assessed the electrical model under full charge/discharge at high currents levels.

Keywords

Supercapacitor, characterization, Impedance Spectroscopy, Constant Current charge/discharge, modelling

Introduction

Supercapacitors are electrical energy devices with high power density and high expected reliability.

They express more temperature stability than other energy storage devices. As a consequence cycles are possible with high charge/discharge currents. Nowadays they become an attractive alternative storage device for several applications. They may be used as the only energy and power device or in combination with other energy supplies like batteries [1], fuel cells [2]…

Some electrical applications like railway [3], [4] and electrical traction systems present high dynamics constraints. In such case, accurate electrical modelling with adaptive characterization methods are necessary. Consequently, we have proposed Impedance Spectroscopy technique [5] in combination with Direct current method.

Impedance spectroscopy technique provides a powerful tool of analysis and investigation of dynamics behaviour of supercapacitor according to dynamic constraints [6]. In addition charge/discharge method allows assessing model validity under high current constraints.

Some mathematical transformations are necessary to find a representative equivalent electric circuit.

More Impedance spectroscopy allows detecting the state of charge of the supercapacitor at any working point.

Ideally, electrical parameters of any electrical model must reflect physical and electrochemical phenomena of supercapacitor. It may be allows observation and comprehension of the evolution of the state of health of supercapacitor under current or power cycling and with ageing.

In this paper we use impedance spectroscopy technique to characterize supercapacitors. We define its metrology [7] and we present and we discuss it. It responds to practice requirements in time of measurements, precision and covering different properties of the supercapacitor under test. On the other hand we propose electrical model based on homogenous porous electrode impedance.

A supercapacitor with carbon/carbon electrodes and organic electrolyte is characterized using impedance spectroscopy method at different voltages. Correlation between impedance spectroscopy measurements and full charge discharge at high current level (100 A, 200A, 400A) is investigated.

Measurement techniques

Impedance spectroscopy technique consists to excite the system under test with small alternative signal (voltage or current) and to measure the other part (current, voltage).

In fact the operating mode for characterization of supercapacitor is the potentiostatic mode, it consists to apply DC voltage V to the system which must be regulated and controlled during the impedance measurement. An alternative sinus AC voltage U(ω)with small amplitude and with pulsation ω (frequency f)

perposed to DC voltage V already stabilized.

is su

U (ω) = Uo e^i(ωt+α) We measure the alternative current

I (ω) = Io e ^i(ωt+δ) We calculate the impedance

Z (ω)= dU(ω) / dI(ω)= Zo e ^{i ϕϕ}

Where the impedance amplitude is calculated as a ratio between the alternative voltage amplitude and the alternative current amplitude, and the phase of the impedance is calculated as a difference between alternative signals arguments.

By varying the frequency of the alternative AC voltage signal we obtain a spectrum of impedance versus frequency. Numerous representations of the impedance spectrum exist: BODE diagram, complex plane diagram (NYQUIST plot) …

The alternative AC voltage magnitude is optimized according to some constraints:

o Minimization of noise on alternative voltage and current signals.

o No violating of the linearity of the system response region in the U/I characteristic.

o Characteristics of supercapacitor in particular its low impedance.

o Technical hardware specifications of the impedancemeter (maximal current, maximal voltage…) One problem inherent in impedance experiments is the balance between the improvement in the data quality obtained by increasing the number of frequencies uses and the number of cycles collected at each frequency and the increase of the time required for the full experiment. This problem is mainly observed when low frequencies are used. The THALES software of the IM6 impedancemeter offers a partial solution by dividing the frequency range into two: high frequency range (f > 66 Hz) and low frequency range (f < 66 Hz).

At high frequencies we calculate impedance as the mean value of impedances calculated for numerous cycles (10 cycles) at the same frequency to increase the quality of data measurement. At low frequencies although the precision is respected the time of measurement is limited at one cycle at each frequency. The total time impedance measurement is realistic for our laboratory uses.

The frequency spectra are chosen in the range between 10 mHz and 50kHz which corresponds to typical time constants in most high power applications.

DC voltage applied to supercapacitor is sufficiently stabilized before starting impedance spectroscopy measurements.

Limitation in high frequencies for low impedance supercapacitors

Some errors appear in low impedance supercapacitors at high frequencies. They are caused by the coupling effects between current feeding and potential sensing lines [8]. They diminish at low frequencies but become dramatic at high frequencies. In practice the use of one twisted wires for current feeding lines and second one for potential sensing lines can help to minimize such errors on measurements.

In spite the careful taking on connections, errors on measurements are minimized but not eliminated. Some complementary methods to spectroscopy measurement exist in literature like High current interrupt method [9].

We have proposed a solution represented in Fig. 1. We have separated voltage sensors from power source according to Ampere’s law. Theoretically the electromagnetic filed in the exterior of the cylinder is equal to zero.

Cylinder

Power (AC current) Cylindrical Supercapcitor

Measurement voltage Fig. 1 Basic scheme of system minimizing electromagnetic coupling effect on impedance spectroscopy

measurements Insulation

Supercapacitors, instrumentation

The two testing methods (impedance spectroscopy and constant current charge/discharge were applied to two supercapacitors B, and F based on activated carbon and organic electrolyte developed for power applications.

B is supercapacitor rated 2600 F of capacitance and 2.5 V of voltage, F is rated 2600 F of capacitance and 2.7 V of voltage.

Impedance spectroscopy measurements are realised with Zahner IM6+PP240 impedance analyzers [10][11].

THALES software ensured the data acquisition and the control function with good quality [12].

We have developed a constant charge/discharge test bench for supercapacitors characterization in our laboratory.

Measurements results and modelling

Impedance Spectroscopy results and discussions

Two supercapacitors E (2600F, 2.5V) and F (2600 F, 2.7 V) are tested with impedance spectroscopy method.

Figure2 illustrate an example of complex plane plot of impedance spectroscopy behaviour of supercapacitors E at different temperatures at voltage of 2 V in the frequency range from 10 mHz to 1kHz.

In contrast figure 4(a, b) represent the behaviour of E and F supercapacitors at different DC voltages at a temperature of 25° C in the frequency range from 10 mHz to 1 kHz.

03965901070 (INRETS - LTN 2004)

0 0,001 0,002 0,003 0,004 0,005 0,006 0,007 0,008 0,009 0,01

0,0002 0,00025 0,0003 0,00035 0,0004 0,00045 0,0005 0,00055 0,0006

Re Z (Ohm)

- Imaginary Z (Ohm) (O

U = 0 V U = 0.5 V U = 1 V U = 1.5 V U = 2 V U = 2.5 V

f = 10 mHz

f = 67 Hz

03965901070 (INRETS - LTN 2004)

0 0,0005 0,001 0,0015 0,002 0,0025 0,003 0,0035 0,004 0,0045 0,005

0,0001 0,0002 0,0003 0,0004 0,0005 0,0006 0,0007 0,0008 0,0009 0,001 Re Z (Ohm)

- Imaginary Z (Ohm)

T = - 25 ° C T = - 10 ° C T = 0 °C T = 25 °C T = 35 ° C T = 45 ° C T = 55 ° C f = 10 m Hz

f = 54.7 m Hz

f = 67 Hz

U = 2 V

Fig. 2 Complex plot of Impedance spectroscopy measurements data for B (2600F, 2.5V) supercapacitor at different voltages (T = 25°C) and at different temperatures (U = 2V)

Simple Pore Model of cylindrical supercapacitor

Fig. 3 gives frequency behaviour of a supercapacitor with homogenous porous electrode at stabilized voltage. We consider pore size accessible with uniform dimensions, and inaccessible pores behaving like a resistance contributing in self discharge. As consequence the impedance of the electrode is equivalent to cylindrical pore impedance in parallel with resistance.

The structure of supercapacitor can be decomposed to three elements [13], [14] : inductor L, series resistance R_s, and complex pore impedance Z_P (jω) (cf. Fig. 4, Fig. 5)

Fig. 3 Complex plane plot of a porous ideally polarizable electrode in series with Rs

Fig. 4 Equivalent circuit for supercapacitor at constant voltage

Fig. 5 Equivalent circuit of Z witch depends to four parameters

Series resistance Rs Complex pore impedance ZP(jω) Inductance L

0 0,0001 0,0002 0,0003 0,0004 0,0005 0,0006 0,0007 0,0008 0,0009 0,001

005

- Imaginary Zp (Ohm)

0 0,0001 0,0002 0,0003 0,0004 0,0

Re al Zp (Ohm ) Rs

-1/jωCdl

Rs +Re l/3

ω

45°

Cdl/2

R1

Cdl/2

R2

Cdl/2

C

Rn

L Rs

dl

n n C

R .

2

2

2 π

τ

⋅

= ⋅ Cdl

R² 2 π². τ

= ⋅ Cdl

R .

2

1 π2

τ

= ⋅

Z

Z

The mathematical expression of ZP (jω) can be given by

s s s C

Z

dl

P

× ×

= × τ

τ

τ coth

) (

We put

C

K ₌ τ

1 and

Cdl K ₌ τ

2 ,

K s K s

s K Z

1 1

coth

)

( = ×

The inverse transformation of Zp(s) in the time domain is given by [14]

∑

+

=

k n

P

k k e

k k t

Z

12 2 2

2 2 1 2

2

1

2

) (

π

,

^Z

^{t =} _C

⁺ _C

∑ ^e

2 2

2 ) 1

(

π

dl

n

n C

R .

2

2 2

π

τ

⋅

= ⋅

∑

=

+

=

1 . 2

2 ) 1

(

n

C t R dl

P

t C

C e

Z

with

τ = C

⋅ R

Where C_dl (average double layer capacitance) is the capacitance at low frequencies, Tau (τ) depends on C_dl and the electrolyte resistance filled in pore R_el. Z_P(jω) is approximated by a n. RC circuits which are fully described by two parameters (C_dl, and τ), it describe in-pore diffusion. So for the totally model of supercapacitor we need to identify four parameters (L, R_s, C_dl, R_el)

Analysis

According to the physic’s theory of Gouy, Chapman and Stern [15],[16],[17] on double layer capacitor, the capacity C_dl is equivalent to two parallel capacities. We note V the voltage on the extremities of the double layer. The dependency of C_dl to the voltage is expressed by

1

1 2

3 cosh( )

1

1 ⁻

⎟⎟⎠

⎜⎜ ⎞

⎝

⎛ + ⋅

= C C C V

C_dl

We have defined the parameters of the capacity Cdl (C3, C2, C1) for B supercapacitor at different temperatures Table. 1) Simulated curves of the double layer capacity Cdl and values of Cdl calculated from impedance spectroscopy measurements show a great agreement (cf. Fig. 6)

The accessibility of the electrolyte within pores depends on molecular electrolyte dimensions and pore size, it varies with temperature. The electrolyte resistance may be a good indicator for electrolyte-pore accessibility. Its behaviour can reflect supercapacitor’s dependency of supercapacitor to temperature.

We note T is the supercapacitor temperature (° K).The dependency expression of the electrolyte resistance R_el to temperature can be given by

) exp(₁

2

3 r r T

r

R_el = + × ×

We have defined the function’s factors (r₁, r₂, r₃) for B supercapacitor at different voltages (cf. Table. 2) Simulated curves of electrolyte resistance R_el and values of R_el calculated from impedance spectroscopy measurements show a great agreement (cf. Fig. 7)

By using the expression of C_dl defined above, we have compared constant current discharge measurement voltage with model simulated voltage. We observe a good concordance between model and constant current discharge Table. 3. Time discharge is limited by our test bench. To enhance the assessment of the validity of our modelling, we have done other experiences in Cegely Laboratory. Model is assessed to full charge/discharge measurements of supercapacitor at high currents levels (100A, 200A, 400A).

1500 1700 1900 2100 2300 2500 2700 2900 3100 3300 3500

0 0.5 1 1.5 2 2.5 3

Voltage (V)

Capacitance Cdl (F)

T =- 25°C : Cdl calculated from IS meas urements T =- 10 °C : Cdl calculated from IS measurements T =- 0 °C : Cdl calculated from IS measurements T = 25°C : Cdl calculated from IS measurements T = 25 °C : Approximation

T = 35°C : Cdl calculated from IS measurements Cdl calculated from IS measurements T = 55°C : Cdl calculated from IS meas urements

Fig. 6 Behaviour of capacitance Cdl with voltage at different temperatures

Table. 1 Approximation function of Cdl parameters at different temperatures

0 0.00025 0.0005 0.00075 0.001 0.00125 0.0015 0.00175 0.002 0.00225

240 250 260 270 280 290 300 310 320 330 340

Temperature (°K)

Resistance Rel (Ohm)

Tension = 0 V : Rel calculated from IS measurements Approximation

Tension = 0.5 V : Rel calculated from IS measurements Approxiamation

Tension = 1 V : Rel calculated from IS measurements Approximation

Tension = 1.5 V : Rel calculated from IS measurements Approximation

Tension = 2 V : Rel calculated from IS measurements Approximation

Tension = 2.5 V : Rel calculated from IS measurements

Fig. 7 Behaviour of electrolyte resistance Rel with temperature at different voltages

Table. 2 Approximation function of electrolyte resistance Rel at different voltages

Table. 3 Difference between of measured voltage and model voltage in the time domain under constant current discharge for B supercapacitor at different

temperatures Assessment of electrical model

Constant current charge/discharge method is the most straightforward method. It requires the application of a current step charge/discharge to the supercapacitor from initial stabilized voltage.

The voltage response as function of time is measured by four wires method. In practice we heave applied full charge/discharge current to the supercapacitor B between 0V and 2.5 V with three current’s level (100A, 200A, 400A) and full discharge between 2.7V and 0V for F(2600F, 2.7V) supercapacitor with two current level (300A, 500A) at ambient temperature (25 °C).

Comparison between measurements and simulations is represented in Fig. 8. It shows differences less than 2 % in the worst case.

T (°C) C1 (F) C2 (F) C3 (F) -25 11..1199 44338877 33333311 -10 11..11 44441144 34340033 0 11..4488 44888811 30308822 25 11..55 44225500 31319900 35 11..3355 44777711 31310088 45 11..4422 44880000 31310088 55 11..3399 44889977 30305533

Voltage

(V) r1 r2 r3

0 --00..003355 6.6.448833 00..000000335566 0,5 --00..003355 6.6.554422 00..000000336611 1 --00..003333 3.3.990088 00..000000337777 1,5 --00..003311 1.1.888844 00..000000338877 2 --00..0033 2.2.114444 00..000000442211 2,5 --00..003355 99..4455 00..000000551177

Temperature (°C)

Current (A)

Discharge time (s)

Max ((V_measured-V _si

/V ^mulated

)

nom ) (%) 500 3 0.4 -25 300 5 0.5 500 3 0.2 -10 300 5 0.4 500 4 0.2 0 300 5 0.2 500 4 1.2 25 300 5 0.6 500 3 0.4 35 300 5 0.8 500 3 0.4 45 _{300 5 0.8} 500 3 0.2

55 _{300 5 0.4}

Fig. 8 Comparison between measured voltage and simulated voltage under full charge/discharge with three levels currents (100 A, 200 A, 400 A)

The difference observed between measurements and simulations may be explained by:

• The model proposed is based on the mean value of capacity of homogenous porous electrode with uniform pore size. It gives good approximation and results. In fact the electrode presents a pore size distribution not uniform.

• The model proposed take into account the in pore diffusion or frequency diffusion, but it neglect the pore size diffusion, observed in low frequencies [18][19].

• The precision of our instruments in the order percentage of the difference observed between measurements and simulations.

Conclusions

We proposed in this work a simplified method to avoid effect coupling in spectroscopy measurements. Indeed we have defined a measurement procedure. It is practice and precise.

The electric model gives a good agreement between measurements and simulations. It is based on physical phenomena. It is very interesting to model supercapacitors in good state of health.

We have modelled in-pore dispersion with frequency, a complete model witch takes into a count pore size dispersion will be proposed in our next papers.

The measurement voltage and the model voltage give a good agreement. It introduces the dependency of capacitance Cdl, resistance RHF and τ to voltage and temperature.

References

[1] Alfred Ruffer, “Le supercondensateur et la batterie se marient pour fournir de l’énergie électrique”, LEI, EPFL.

[2] R. Kötz, S. Müller, M. Bärtschi, B. Schnyder, P. Dietrich, F. N. Büchi, A. Tsukada, G. G. Scherer, P. Rodatz, O.

Garcia1, P. Barrade, V. Hermann, R. Gallay, “Supercapacitors for peak power demand in fuel-cell driven cars” . [3] A. Hammar, R. Lallemand, G. Coquery, J. Chabas, P. Venet, G. Rojat, ‘Assessment of electrothermal model of

supercapacitors for railway applications’ EPE 2005 Dresden, September 2005.

[4] Jean Chabas, Gérard Coquery. THALES: hybrid tram-train using ultracapacitors for electric power supply, PROSPER’01, September 2001

[5] S. Buller, E. karden, D. Kok, and R. W. De Doncker, “Modelling the dynamic behaviour of supercapacitors using impedance spectroscopy”. 2001.

[6] Eckhard Karden, Stephan Buller, Rik W. De Doncker, “A frequency-domain approach to dynamical modelling of electrochemical power sources”, Electrochimica Acta, pp 2347-2356, N°47 2002.

[7] A. Hammar, J. Chabas, R. Lallemand, G. Coquery, G. Rojat, P. Venet, ‘Impedance Spectroscopy characterization of supercapacitors for railway environment’, SAAEI/EPF, Toulouse, September 2004

[8] C.A. Schiller, “Main error sources at AC measurements on low impedance objects”, Electrochemical Applications, PP. 10-12, 1997

[9] F. Richer, C-A Schiller , N.Wagner, “Current interrupt technique measuring low impedances at high frequencies”, Electrochemical applications 2002

[10] www.Zahner.de

[11] Electromechemical applications. Advances in electrochemical applications of impedance spectroscopie. ZAHNER- elektrik mbH & Co. KG in June 2002

[12] Adrian W. Bott, “Electrochemical Impedance Spectroscopy using the BAS-Zahner IM6 and IM6e Impedance Analyzers”, Current Separations, pp. 53-59, 1998.

[13] R. De Levie. Electrochemical response of porous and rough electrodes, Advances in electrochemistry and Electrochemical Engineering, pp. 329-397, vol. 6, Wiley Interscience, 1967.

[14] Murray R. Spiegel. Transformées de Laplace, pp. 264, Serie Schaum, 1980.

[15] G.Gouy, J. Phys., 9 (1910) 457.

[16] DL. Chapman, Philos. Mag., 25 (1913) 475.

[17] O. Stern, Z. Electrochem., 30 (1924) 508

[18] Hyun-Kon Song, Joo-Hwan Sung, Yong-Ho Jung, Kun-Hong Lee, Le H. Dao, Myung-Hwan Kim,

‘Electrochemical porosimetry’, Journal of the electrochemical society, 151 (3) E102-E109 2004.

[19] Hyun-Kon Song, Hee- Young Hwang, Kun-Hong Lee, Le H. Dao, ‘The effect of pore size distribution on the frequency dispersion of porous electrodes’